use 5.010;
use strict;

our $FOO;

BEGIN {
    $FOO = 'still foo';
}

sub FOO () { 'foo' }

BEGIN {
    *BAR = *FOO;
    say "in BEGIN (1): \$FOO = '$FOO'";
    undef *FOO;
    say "in BEGIN (2): \$FOO = '$FOO'"; 
    *FOO = *BAR{SCALAR};
    undef *BAR;
}
say defined &FOO ? 'subroutine defined' : 'subroutine undef';
say eval 'my $false; FOO if $false; 1'
    ? 'FOO allowed'
    : 'FOO not allowed'
;
say $FOO;
__END__
in BEGIN (1): $FOO = 'still foo'
in BEGIN (2): $FOO = ''
subroutine undef
FOO not allowed
still foo
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update: tweaked the code to more closely resemble the OP's.

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}